Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.annf)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=11/2, a₂>=11/2

For fixed z and a₁=11/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=11/2, a₂=11/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.annf.01

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(11/2), 2}, z] == (1/9282994875) (E^(z/2) (9282994875 - 29797267500 z + 50328507600 z^2 - 68936767200 z^3 + 97786634400 z^4 - 185301043200 z^5 + 878066179200 z^6 + 3471971247360 z^7 + 3294011508480 z^8 + 1405635517440 z^9 + 321205463040 z^10 + 42236866560 z^11 + 3266310144 z^12 + 145457152 z^13 + 3424256 z^14 + 32768 z^15) BesselI[0, z/2]) + (1/9282994875) (E^(z/2) (-1489863375 + 11851037100 z - 24190261200 z^2 + 34295335200 z^3 - 45842176800 z^4 + 71621625600 z^5 - 173806093440 z^6 + 1582405735680 z^7 + 2265653617920 z^8 + 1139043333120 z^9 + 283457771520 z^10 + 39178727424 z^11 + 3125891072 z^12 + 142082048 z^13 + 3391488 z^14 + 32768 z^15) BesselI[1, z/2])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]